If x - y = 2 and xy = 15 then the value of (x² + y²) is?

Question: If x - y = 2 and xy = 15 then the value of (x² + y²) is?

Solution:
Given that,
x - y = 2
and xy = 15

Now,
x - y = 2
⇒ (x - y)² = 2²
⇒ x² - 2xy + y² = 4
⇒ x² + y² - 2 × 15 = 4
⇒ x² + y² - 30 = 4
⇒ x² + y² = 4 + 30
∴ x² + y² = 34